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Chapter 34: Q. 53 (page 992)

An astronaut is exploring an unknown planet when she accidentally drops an oxygen canister into a 1.50-m-deep pool filled with an unknown liquid. Although she dropped the canister 21 cm from the edge, it appears to be 31 cm away when she peers in from the edge. What is the liquid鈥檚 index of refraction? Assume that the planet鈥檚 atmosphere is similar to earth鈥檚

Short Answer

Expert verified

Refractive index of the liquid is 1.46

Step by step solution

01

Step 1. Given information is :Depth of the pool = 1.50 mCanister is 21 cm from the edgeCanister's image from the astronaut is 31 cm from the edgeRefractive index of earth's air, n = 1.00

We need to calculate the refractive index of the liquid.

02

Step 2. Using the concepts of divergence and snell's law.

Refraction of the rays away from the normal and diverging outwards, along with the image point of the canister is shown below :

As per the diagram,

tan胃1=21cm150cm胃1=tan-121150胃1=7.97掳

胃2is represented as :

tan胃2=31cm150cm胃2=tan-131150胃2=11.7掳

Using Snell's Law,

nliquidsin胃1=nairsin胃2nliquid=nairsin胃2sin胃1nliquid=(1.00)sin11.7掳sin7.97掳nliquid=1.46

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Most popular questions from this chapter

A 1.0-cm-tall object is 20cmin front of a convex mirror that has a 60cmfocal length. Calculate the position and height of the image. State whether the image is in front of or behind the mirror, and whether the image is upright or inverted.

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A 5.0鈭�cm-thick layer of oil is sandwiched between a 1.0鈭�cm thick sheet of glass and a 2.0鈭�cm-thick sheet of polystyrene plastic. How long (in ns) does it take light incident perpendicular to the glass to pass through this 8.0鈭�cm-thick sandwich?

A 1.0-cm-tall object is 75cmin front of a converging lens that has a 30cmfocal length.

a Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.
bCalculate the image position and height. Compare with your ray-tracing answers in part a.

There鈥檚 one angle of incidence 尾onto a prism for which the light inside an isosceles prism travels parallel to the base and emerges at angle 尾.

a. Find an expression for 尾in terms of the prism鈥檚 apex angle 伪and index of refraction n.

b. A laboratory measurement finds that 尾= 52.2掳 for a prism shaped like an equilateral triangle. What is the prism鈥檚 index of refraction?
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